Finite Element Methods For Semilinear Parabolic Initial,Boundary Value Problems With Singularities

The patial differential equations with singular coefficients are very important ones in the field of numerical mathematics. In recent years, many researchers have studied such kinds of problems by all different numerical methods and achieved excellent results. In this article, a class of semilinear parabolic problems with singularities was considered. First of all,we made the equation be linear,and proved the existence and uniqueness of the generalized solution, results of the FEM solution error bounds, with respect to semi-discrete and whole-discrete problems , are obtained respectively. Lastly, we gave out the linear modified results of Crank-Nicolson-Galerkin method.